非定域变换的广义Ward恒等式

基于高阶微商奇异拉氏量系统相空间Green函数的生成泛函,导出了该系统在定域和非定域变换下的广义正则Ward恒等式.对规范不变系统,从位形空间生成泛函出发,导出了该系统在定域、非定域和整体变换下的广义Ward恒等式.用于高阶微商非Abel(Chern-Simons CS)理论,无需作出生成泛函中对正则动量的路径积分,即可导出正规顶角的某些关系.此外还给出了BRS变换下的Ward-Takahashi恒等式.     

Ward恒等式在量子电动力学重正化中的应用

Ward恒等式是一个连接逆向费米子传播子和费米子—光子顶角的等式 ,论述了Ward恒等式在量子电动力学 (QED)中的应用。     

高阶微商场论中奇异拉氏量系统的量子正则对称性

给出了高阶徽商场论中奇异拉氏量系统规范生成元的构成.从相空间中Green函数的生成泛函出发,导出了约束Hamilton系统正则形式的Ward恒等式.指出该系统的量子正则方程与由Dirac猜想得到的经典正则方程不同.给出了与Chern-Simons理论等价的一个广义动力学系统的量子化.将正则Ward恒等式初步应用于该系统,不作出对正则动量的路径积分,也可导出场的传播子与正规顶角之间的某些关系.     

高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

相空间路径积分中的Feynman规则和广义Ward恒等式

基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变.     

正则形式的SU(N)规范理论的约束关联动力学(Ⅲ)等时关联Green函数的运动方程与二体关联近似

把多时关联Green函数的运动方程转变成等时关联Green函数的运动方程,其中包括夸克和胶子的密度矩阵的运动方程以及顶角函数的运动方程.在二体关联截断近似下,给出运动方程、高斯定律和Ward恒等式的明显表达式.     

正则Ward恒等式和Abel规范理论中动力学质量的产生

文中基于约束Hamilton系统理论用Faddeev-Senjanovic路径积分量子化方法,重新讨论了Cornwall-Norton和Jackiw-Johnson模型的量子化,导出了这两个系统的正则Ward恒等式,利用导出的正则Ward恒等式,得到了包括费米子和束缚态的质量谱.所得的结果与其他方法导出的结果相同     

BJL技术与阿贝尔陪集纯规范场理论手征反常的微扰论研究

本文首次进行了陪集纯规范场理论的微扰论研究.利用BJL技术,通过计算有关对易子的Schwinger项,得到了阿贝尔陪集纯规范场理论中的反常Ward恒等式.这一结果与相应的非微扰计算相符合.     

规范场-鬼场固有顶角的Ward-Takahashi恒等式

本文推导了规范场-鬼场固有顶角满足的 Ward-Takahashi 恒等式的便于应用的形式并举例讨论了它的应用。     

1+1维非线性σ模型的BRST变换的等价性和Ward恒等式

在依据Dirac约束规范理论和作推广后的条件下,导出了规范生成元,推导出了1+1维O(3)非线性σ模型的一般条件(β≠0)下的BRST变换,给出了其BRST变换与Dirac规范变换的等价关系,得到了鬼场的新的一般对易关系,且其一般参数β为零时就回到通常的鬼场的对易关系.并由规范生成元导出了BRST荷,进而完成了此模型的一种BRST量子化.还在此基础上进一步导出了此系统的Green函数生成泛函、连通Green函数生成泛函和正规顶角生成泛函,获得了3种不同的Ward恒等式     

WARD IDENTITIES IN PHASE SPACE AND THEIR APPLICATIONS

Starting from the phase space path integral, we have derived the Ward identities in canonical formalism for a system with regular and singular Lagrangian. This formulation differs from the traditional discussion based on path integral in configuration space. It is pointed out that the quantum canonical equations for systems with singular Lagrangians are different from the classical ones obtained from Dirac's conjecture, The preliminary applications of Ward identities in phase space to the Yang-Mills theory are given. Some relations among the proper vertices and propagators are deduced,the PCAC, AVV vertices and generalized PCAC expressions are also obtained. We have also pointed out that some authors in their early work had ignored the treatment of the constraints.     

Canonical symmetry of a constrained Hamiltonian system and canonical ward identity

An algorithm for the construction of the generators of the gauge transformation of a constrained Hamiltonian system is given. The relationships among the coefficients connecting the first constraints in the generator are made clear. Starting from the phase space generating function of the Green function, the Ward identity in canonical formalism is deduced. We point out that the quantum equations of motion in canonical form for a system with singular Lagrangian differ from the classical ones whether Dirac's conjecture holds true or not. Applications of the present formulation to the Abelian and non-Abelian gauge theories are given. The expressions for PCAC and generalized PCAC of the AVV vertex are derived exactly from another point of view. A new form of the Ward identity for gauge-ghost proper vertices is obtained which differs from the usual Ward-Takahashi identity arising from the BRS invariance.     

Chiral Symmetry,Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional Chiral Gross-Neveu Model

Chiral Ward-Takahashi identities with composite fields are applied to investigate mass spectra in (2+1) dimensional chiral Gross-Neveu model.The fermion mass and bound state spectra are obtained,which are in agreement with large-N expansion in the lowest approximation.When the chiral symmetry is an approximate one,we obtain the PCAC.     

On the validity of ward identities

Ward identities for matrix elements of covariant two-point time-ordered operators in the presence of an arbitrary number of subtractions are investigated. Neither the existence of naiveT-products nor the existence of equal-time commutators between current densities will be assumed. It is shown by means of the Jost-Lehmann-Dyson representation thatT*-products can always be defined such that normal Ward identities with respect to one current are valid. The simultaneous validity of normal Ward identities with respect to two currents requires a relation between equal-time charge-current commutators.Our results show that the usual realization of current algebra in the form of Ward identities is possible even if subtractions are necessary. Some examples are discussed in detail.     

Gauge dependence of effective potential and self-consistent dimensional reduction

The gauge dependence of the effective potential determining the Kaluza-Klein radius self-consistently is contrasted to that belonging to a gauge theory with spontaneous symmetry breaking at finite temperature. Formally the two quantities are computed in the same way and obey the same Ward identities, but a gauge-independent approximation scheme is possible only in the latter case because of the coupling between the Goldstone field and the longitudinal vector field. The connection to the Ward identities of the two theories is also obtained.     

Quantal global symmetry for a gauge-invariant system

Based on the configuration-space generating functional obtained by using the Faddeev-Popov trick for a gauge-invariant system, the Ward identities for global transformation are derived. The conservation laws at the quantum level for global symmetry transformation are also deduced. A preliminary application of the present formulation to non-Abelian Chern-Simons (CS) theory is given. The Ward identity and quantal BRS charge under the BRS transformation are deduced. The quantal conserved angular momentum is obtained and the fractional spin for CS theories is discussed.     

Conformal spinor current anomalies

An anomalous divergence of the conformal spinor current is obtained for some massless supersymmetric theories. The corresponding modified Ward identities are discussed for a simple model without gauge fields.     

Renormalization of an abelian gauge theory in stochastic quantization

The renormalization of an abelian gauge field coupled to a complex scalar field is disccused in the stochastic quantization method. The supper space formulation of the stochastic quantization method is used to derived the Ward Takahashi identities assocoated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahshi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constant in temrs of scaling of the fields and of the parameters appearing in the stochastic theory.